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Discrete Itô Formula for Delay Stochastic Difference Equations with Multiple Noises

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Recent Advances in Delay Differential and Difference Equations

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 94))

Abstract

For stochastic difference equation with multiple noises, finite delays and a parameter h we prove a variant of discrete Itô formula. Then we apply the formula to derive conditions which provide either P{lim n → ∞ x n  = 0} = 1 or P{liminf n → ∞  | x n  |  > 0} = 1, where x n is a solution of the equation with sufficiently small parameter h.

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References

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Acknowledgements

The author thanks the anonymous referee for encouraging remarks and useful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of the West Indies, Kingston 7, Jamaica

    Alexandra Rodkina

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  1. Alexandra Rodkina
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Correspondence to Alexandra Rodkina .

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Editors and Affiliations

  1. Department of Mathematics, University of Pannonia, Veszprém, Hungary

    Ferenc Hartung

  2. Department of Mathematics, University of Pannonia, Veszprém, Hungary

    Mihály Pituk

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Rodkina, A. (2014). Discrete Itô Formula for Delay Stochastic Difference Equations with Multiple Noises. In: Hartung, F., Pituk, M. (eds) Recent Advances in Delay Differential and Difference Equations. Springer Proceedings in Mathematics & Statistics, vol 94. Springer, Cham. https://doi.org/10.1007/978-3-319-08251-6_10

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